UPDATE 2: NBC News again adjusts the timing of Rosenstein's expected departure:
A source close to Rosenstein said he intends to stay on until Mueller's investigative and prosecutorial work is done. The source said that would mean Rosenstein would remain until early March. Several legal sources have said they expect the Mueller team to conclude its work by mid-to-late February, although they said that timeline could change based on unforeseen investigative developments.
The source said once Mueller's work is done, the special counsel's report to the Justice Department would follow a few weeks later, and Rosenstein would likely be gone by then.
Rod Rosenstein, who oversaw Mueller probe, leaving DOJ after investigation wraps up (NBC News)
UPDATE: NBC News now saying Rosenstein plans to say until Mueller submits his report.
A source close to Rosenstein said he intends to stay on until Mueller submits a report to the Justice Department on the Russian meddling investigation. The source said that would mean Rosenstein would remain until early March. Several legal sources have said they expect the Mueller team to submit its report by mid-to-late February, although they said that timeline could change based on unforeseen investigative developments.
NBC News' Intelligence and national security reporter:
Rod Rosenstein, who oversaw Mueller probe, leaving Justice Department (NBC News)
Deputy Attorney General Rod Rosenstein, who appointed Special Counsel Robert Mueller and has been overseeing the Russia investigation, is planning to leave the Justice Department shortly after a new attorney general, presumably President Trump's nominee William Barr, is confirmed.
Sources told ABC News Rosenstein wants to ensure a smooth transition to his successor and would accommodate the needs of Barr, should he be confirmed.
Rosenstein apparently had long been thinking he would serve about two years, and there was no indication that he was being forced out at this moment by the president.
Barr, who served in the position in the early 1990s and is President Donald Trump’s pick to do the job again, has a confirmation hearing before the Senate Judiciary Committee next week and could be in place at the Justice Department as soon as February.
Rosenstein plans to leave at some point after that, though no date has been set and there is no formal plan for the departure, according to the person, who was not authorized to discuss internal conversations publicly and spoke on the condition of anonymity ...
... It is common for new attorneys general to select their own deputies and Barr has told people close to him that he wanted his own No. 2.
(...)
Barr would take over control of the [Mueller] investigation, assuming the same final say over major investigative steps that acting Attorney General Matthew Whitaker has had since former Attorney General Jeff Sessions was ousted in November.
Responding to news of Rosenstein's impending departure, Democratic Sen. Tim Kaine of Virginia told CNN's "New Day" that he has "deep concern" about how Barr will handle the Mueller probe. He referred to a memo Barr wrote in which he was critical of the investigation.
"William Barr was sending freelance memos to the Trump administration making a case to undercut the Mueller investigation," Kaine said. "So the deep concern will be if he comes in and Rosenstein is gone, is this just a preface to either undercutting the investigation or trying to keep the results of it hidden from the American public."
AP source: Rosenstein expected to leave Justice in weeks (AP)
Rod Rosenstein, who oversaw Mueller probe, leaving Justice Department (NBC News)
Rosenstein expected to depart DOJ in coming weeks if new attorney general confirmed (ABC News)